My partner had a permanent visa and was living in England when I met her. We were in a relationship for around 18 months (14 of it living together) when we decided to come to Australia together we then had to prove that we had lived together at least 12 months. I appreciate what others have said but there did not seem to be any alternative to this. We were told repeatedly that we had to provide hard proof that we were in a relationship. This included things like having booked holidays together (Joint names, not necessarily joint account), bank statements, credit card statements, utility bills, mobile bills etc. at the address where we both lived. All these however NOT necessarily in joint names - they simply wanted proof that we were at the same address. I would advise that you talk to immigration and tell them your circumstances. The basic aim is to get as much hard evidence (facts) together to show you are a couple and prove the length of time you have been.
Bear in mind that once you apply there may be a wait of around 5-6 months while your application is processed. This would mean that if you were on a tourist visa you legally wouldn't be able to work for around 8-9 months after your work visa expired. Could you try for sponsorship with your current employer in the meantime?